Question

what is the derivative of -2(ln(3^4x))?

Answer 1

factor out your constant:
-2((d/dx)ln(3^(4x)))
use the chain rule:
((dln(u))/du) (du/dx) where u = 3^(4x)
use the chain rule again:
((d/dx) 3^4x
(d3^u)/du (du/dx)
where u = 4x
factor out your constants:
-2ln(3)(4(d/dx (x)))
derivative of x = 1
d/dx(-2ln(3^(4x))) =
-8ln(3)

Answer 2

thanks!! that is what I got, but my answer key says otherwise.

Answer 3

yeah, you may simplify it further, or may have simplified differently during an intermediate step